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Abstract

The Bayesian inference approach to the inverse problem of spectral signal recovery has been extended to mixtures of Gaussian probability distributions of a training dataset in order to increase the efficiency of estimating the spectral signal from the response of a transformation system. Bayesian (BIC) and Akaike (AIC) information criteria were assessed in order to provide the Gaussian mixture model (GMM) with the optimum number of clusters within the spectral space. The spectra of 2600 solar illuminations measured in Granada (Spain) were recovered over the range of 360–830 nm from their corresponding tristimulus values using a linear model of basis functions, the Wiener inverse (WI) method, and the Bayesian inverse approach extended to the GMM (BGMM). A model of Gaussian mixtures for solar irradiance was deemed to be more appropriate than a single Gaussian distribution for representing the probability distribution of the solar spectral data. The results showed that the estimation performance of the BGMM method was better than either the linear model or the WI method for the spectral approximation of daylight from the three-dimensional tristimulus values.

References

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Table 1.

Spectral and Colorimetric Performance of Spectral Reconstruction Using the Linear Model, the WI Approach, and the Bayesian Inverse Model Extended to the GMM (BGMM)a

Method

% Feasible r^

Median

Mean

Linear

86.04

(0.9997, 0.1689)

(0.9985, 0.3220)

WI

85.69

(0.9998, 0.1688)

(0.9988, 0.2959)

BGMM

99.97

(0.9999, 0.1423)

(0.9990, 0.3069)

a The table shows the percentage of feasible recovered spectra together with the average and median of (GFC, ΔEuv*) measured between spectrum r and the feasible reconstructed r^ for all the 2600 natural illuminations.